Continuity of the Sinai-Ruelle-Bowen measure entropy

TL;DR

This paper investigates the entropy of the Sinai-Ruelle-Bowen measure in convex projective structures, demonstrating that this entropy varies continuously, which enhances understanding of the geometric properties of these structures.

Contribution

It establishes the continuity of the Sinai-Ruelle-Bowen measure entropy in convex projective structures, extending the understanding beyond topological entropy.

Findings

Sinai-Ruelle-Bowen measure entropy is continuous in convex projective structures.

Provides new insights into the geometric analysis of convex projective structures.

Bridges the gap between topological entropy and measure-theoretic entropy in this context.

Abstract

The space of convex projective structures has been well studied with respect to the topological entropy. But, to better understand the geometry of the structure, we study the entropy of the Sinai-Ruelle-Bowen measure and show that it is a continuous function.